Problem Statement

There is a grid with $H$ rows and $W$ columns where each square has one of the characters X and Y written on it. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left. The characters on the grid are given as $H$ strings $S_1, S_2, \dots, S_H$: the $j$-th character of $S_i$ is the character on square $(i, j)$.

You can set up fences across the grid between adjacent rows and columns. Fences may intersect. After setting up fences, a block is defined as the set of squares reachable from some square by repeatedly moving up, down, left, or right to the adjacent square without crossing fences. (See also Sample Output 1.)

There are $2^{H-1} \times 2^{W-1}$ ways to set up fences. How many of them satisfy the following condition, modulo $998244353$?

Condition: Each block has exactly two squares with Y written on it.

Constraints

• $1 \leq H \leq 2000$
• $1 \leq W \leq 2000$
• $S_i \ (1 \leq i \leq H)$ is a string of length $W$ consisting of X and Y.

Input

The input is given from Standard Input in the following format:

H W
S_1
S_2
\vdots
S_H

Output

Print the number of ways to set up fences to satisfy the condition, modulo $998244353$.